FBISE, NCP & NBF-aligned resources for Classes 9–12
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Math Chapter 11 : Topic 4
Probability Applications
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A card is drawn from a standard deck. What is the probability that it is a red card?
Reasoning: There are $26$ red cards out of $52$ total cards.$\ \ \ \Longrightarrow \ \ \ (26/52 = 1/2)$
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A die is rolled. What is the probability of getting a number greater than $4$?
Reasoning: Numbers greater than $\ 4\ $ are $\left\{ 5,\ 6 \right\}\ \ \ \Longrightarrow \ \ \ \ 2$ outcomes out of $\ 6\ \ \ \Longrightarrow$$(2/6 = 1/3)$.
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A bag contains $3$ red, $5$ blue, and $2$ green balls. What is the probability of selecting a green ball?
Reasoning: Total balls $= 10$, green $= 2\ \ \ \ \Longrightarrow \ \ \ \ (2/10 = 1/5)$
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A student guesses an answer randomly on a $4$-option $MCQ$. What is the probability of guessing correctly?
Reasoning: Only $1$ correct option out of $4\ \ \ \ \Longrightarrow \ \ \ \ (1/4)$
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A coin is tossed twice. What is the probability of getting exactly one head?
Reasoning: Outcomes: $HH$, $HT$, $TH$, $TT$Favorable: $HT$, $TH\ \ \ \ \Longrightarrow \ \ \ \ 2/4 = 1/2$
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A box contains $6$ apples and $4$ oranges. What is the probability of selecting an orange?
Reasoning: Total fruits $= 10\ \ \ \ \Longrightarrow \ \ \ \ $oranges $= 4\ \ \ \ \Longrightarrow \ \ \ \ (4/10 = 2/5)$
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A number is selected from $1$ to $10$. What is the probability that it is even?
Reasoning: Even numbers $= 2,4,6,8,10\ \ \ \Longrightarrow \ \ \ 5$ out of $10\ \ \ \Longrightarrow \ \ \ $ $\left( \frac{5}{10} = \frac{1}{2} \right)$
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A spinner has $8$ equal sections numbered $1 - 8$. What is the probability of landing on a prime number?
Reasoning: Primes: $2,3,5,7\ \ \ \ \Longrightarrow \ \ \ \ 4$ out of $8\ \ \ \ \Longrightarrow \ \ \ \ (1/2)$
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A card is drawn. What is the probability that it is a king?
Reasoning: $4$ kings out of $52$ cards$\ \ \ \ \Longrightarrow \ \ \ \ (4/52 = 1/13)$
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A jar contains $5$ identical coins, $2$ are biased and always give heads. What is the probability of picking a biased coin?
Reasoning: Favorable $= 2$ biased coins out of $5\ \ \ \ \Longrightarrow \ \ \ \ (2/5)$
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What is the probability of getting a tail when a fair coin is tossed?
Reasoning: Equal chance of head and tail$\ \ \ \ \Longrightarrow \ \ \ \ (1/2)$
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A bag has $7$ white and $3$ black balls. Two balls are drawn one after another without replacement. What is the probability both are white?
Reasoning: $\frac{7}{10} \times \frac{6}{9} = \frac{42}{90} = \frac{21}{45}$
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Probability of an impossible event is:
Reasoning: Impossible events never occur$\ \ \ \ \Longrightarrow \ \ \ \ $probability $= 0$
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Probability of a sure event is:
Reasoning: Certain event always occurs$\ \ \ \ \Longrightarrow \ \ \ \ $probability $= 1$
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A student randomly selects a day of the week. What is the probability it is a weekend?
Reasoning: Weekend $=$ Saturday, Sunday$\ \ \Longrightarrow \ \ 2$ out of $7$ days.
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If $P(A) = 0.3$, what is $P$ (not $A$)?
Reasoning: Complement rule$\ \ \ \ \Longrightarrow \ \ \ \ (1 - 0.3 = 0.7)$
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A number is chosen from $1$ to $20$. What is the probability it is divisible by $5$?
Reasoning: Numbers$\ \ \ \ \Longrightarrow \ \ \ \ 5$, $10$, $15$, $20\ \ \ \Longrightarrow \ \ \ 4\ $ out of $\ 20\ \ \ \Longrightarrow \ \ \ (1/5)$
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Two dice are rolled. What is the probability that the sum is $7$?
Reasoning: Favorable outcomes $= 6\ \ \ \ \Longrightarrow \ \ \ \ (6/36 = 1/6)$
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A drawer contains $10$ socks: $6$ black and $4$ white. What is the probability of picking a white sock?
Reasoning: $(4/10 = 2/5)$
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A card drawn is known to be a face card. What is the probability it is a queen?
Reasoning: Face cards $= 12\ (J$, $Q$, $K)$. Queens $= 4\ \ \ \Longrightarrow \ \ \ (4/12 = 1/3)$
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A student picks a random letter from the word "MATHEMATICS". What is the probability of picking '$M$'?
Reasoning: Total letters $= 11$, $\ M$ appears twice$\ \ \ \ \Longrightarrow \ \ \ \ (2/11)$
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A number is selected from $1$ to $50$. What is the probability it is a multiple of $10$?
Reasoning: Multiples$\ \ \ \Longrightarrow \ \ \ 10$, $20$, $30$, $40$,$\ 50\ \ \ \Longrightarrow \ \ \ 5$ out of $50\ \ \ \Longrightarrow \ \ \ (1/10)$
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A bag contains $4$ red, $4$ blue, and $2$ yellow balls. What is the probability of NOT picking a yellow ball?
Reasoning: Not yellow $= 8$ out of $10\ \ \ \ \Longrightarrow \ \ \ \ (4/5)$
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A die is rolled. What is the probability of getting an odd number?
Reasoning: Odd numbers$\ \ \ \ \Longrightarrow \ \ \ \ 1$, $3$, $5\ \ \ \ \Longrightarrow \ \ \ \ 3$ out of $6\ \ \ \ \Longrightarrow \ \ \ \ (1/2)$
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A number is chosen from $1 - 100$. What is the probability it is less than $25$?
Reasoning: Numbers $1 - 24\ \ \ \ \Longrightarrow \ \ \ \ 24$ out of $100 \approx$ $\left( \frac{24}{100} = \frac{1}{4} \right)$.
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