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Math Chapter 11 : Topic 3
Event Probability
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A die is rolled once. What is the probability of getting an even number?
Reasoning: Even numbers $= \{ 2,\ 4,\ 6\}\ \ \ \ \Longrightarrow \ \ \ \ 3$ outcomesTotal outcomes $= 6\ \ \ \ \Longrightarrow \ \ \ \ $Probability $= 3/6 = 1/2$
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A card is drawn from a deck. Probability of getting a red card is:
Reasoning: Red cards $= 26$ out of $52\ \ \ \ \Longrightarrow \ \ \ \ 26\ /\ 52 = 1/2$
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Probability of an impossible event is:
Reasoning: Impossible events never occur $\Longrightarrow$ Probability $= 0$
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If probability of an event is $0.7$, probability of it not occurring is:
Reasoning: $P\ (not\ A) = 1 - P(A) = 1 - 0.7 = 0.3$
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A bag contains $5$ red and $3$ blue balls. Probability of selecting a red ball is:
Reasoning: Total balls $= 8\ \ \ \ \Longrightarrow \ \ \ \ $Red $= 5\ \ \ \ \Longrightarrow \ \ \ \ $Probability $= 5/8$
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Probability of not getting a head when tossing a coin:
Reasoning: $P\ (Tail) = 1/2$
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If $P(A) = 1$, then event $A$ is:
Reasoning: Probability $= 1$ means event always occurs
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A number is selected from $1$ to $10$. Probability it is greater than $8$:
Reasoning: Numbers $> 8 = \{ 9,10\}\ \ \ \ \Longrightarrow \ \ \ \ 2$ outcomes$\ \ \ \ \Longrightarrow \ \ \ \ 2/10$
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Probability of not selecting a vowel from letters $A$, $B$, $C$, $D$, $E$:
Reasoning: Non-vowels $= B$, $C$, $D\ \ \ \ \Longrightarrow \ \ \ \ 3/5$
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Which relation is always true?
Reasoning: Complementary rule
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A spinner has $4$ equal sections. Probability of landing on one section:
Reasoning: Each section equally likely $\Longrightarrow$ $1/4$
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Probability of selecting a number divisible by $3$ from $1 - 9$:
Reasoning: Multiples of $3\ \ \ \ \Longrightarrow \ \ \ \ 3$, $6$, $9\ \ \ \ \Longrightarrow \ \ \ \ 3/9 = 1/3$
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If $P(A) = 0.25$, then $P$ (not $A$) $=$ _________.
Reasoning: $1 - 0.25 = 0.75$
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A die is rolled. Probability of not getting $6$:
Reasoning: Not $6 = 5$ outcomes $\Longrightarrow$ $5/6$
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Which event has probability closest to $0$?
Reasoning: Impossible $\Longrightarrow$ $0$
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A student randomly selects a day of week. Probability it is not Sunday:
Reasoning: $6$ days are not Sunday
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Probability of selecting an odd number from $1 - 6$:
Reasoning: Odd numbers$\ \ \ \ \Longrightarrow \ \ \ \ 1$, $3$, $5\ \ \ \ \Longrightarrow \ \ \ \ 3/6 = 1/2$
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If an event has no favorable outcomes, its probability is:
Reasoning: No favorable outcomes $\Longrightarrow$ impossible
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A card is drawn. Probability of not getting a king:
Reasoning: Kings $= 4\ \ \ \ \Longrightarrow \ \ \ \ $Not kings $= 48\ \ \ \ \Longrightarrow \ \ \ \ 48/52 = 12/13$
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Which statement is correct?
Reasoning: Basic probability rule
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Probability of selecting a consonant from English vowels $(A$, $E$, $I$, $O$, $U)$:
Reasoning: No consonants present
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A bag has $10$ balls, all red. Probability of selecting a blue ball:
Reasoning: No blue balls
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Probability of getting a number less than $7$ on a die:
Reasoning: All outcomes satisfy condition.
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If $P(A) = 0.6$, then which is true?
Reasoning: Complement rule
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A number is chosen from $1 - 20$. Probability it is not divisible by $5$:
Reasoning: Multiples of $5$:$4$ numbers $\Longrightarrow$ Not divisible $= 16\ \ \ \ \Longrightarrow \ \ \ \ 16/20 = 4/5$
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