If P B = 3 4 , P A ∩ B ∩ C ¯ = 1 3 and P A ¯ ∩ B ∩ C ¯ = 1 3 . Find P B ∩ C .

From the above Venn diagram, P B ∩ C = P B - P A ∩ B ∩ C ¯ - P A ¯ ∩ B ∩ C ¯ = 3 4 - 1 3 - 1 3 = 3 4 - 2 3 = 9 - 8 12 = 1 12 .

If A and B are two independent events such that P A ¯ ∩ B = 2 15 and P A ∩ B ¯ = 1 6 , then find P B .

Let P A = x , P B = y Now, P A ¯ ∩ B = 2 15 ⇒ P B - P A ∩ B = 2 15 ⇒ P B - P A P B = 2 15 ⇒ P B 1 - P A = 2 15 ⇒ y 1 - x = 2 15 . . . i And, P A ∩ B ¯ = 1 6 ⇒ P A - P A ∩ B = 1 6 ⇒ P A - P A P B = 1 6 ⇒ P A 1 - P B = 1 6 ⇒ x 1 - y = 1 6 . . . ii Subtracting i & ii , we get y - x = 2 15 - 1 6 ⇒ x = 1 30 + y Putting in ii , we get 1 30 + y 1 - y = 1 6 ⇒ 1 + 30 y 1 - y = 5 ⇒ 1 + 29 y - 30 y 2 = 5 ⇒ 30 y 2 - 29 y + 4 = 0 ⇒ y = 29 ± 361 60 ⇒ y = P B = 4 5 , 1 6

E M B I B E

Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>EXERCISE 14.2>Q 13

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IMPORTANT

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The odds against a certain event is $5 : 2$ and the odds in favour of another event is $6 : 5$ . If both the events are independent, then the probability that at least one of the events will happen is

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Important Questions on Probability

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>EXERCISE 19.2>Q 13

A

draws two cards with replacement from a deck of

52

cards and

B

throws a pair of dice. The chance that

A

gets both cards of same suit and

B

gets total of

6

is

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>EXERCISE 19.2>Q 14

Two dice are thrown together. The probability that at least one will show its digit

6

is

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>EXERCISE 19.2>Q 16

The probability that

A

speaks truth is

\frac{4}{5}

, while this probability for

B

is

\frac{3}{4}

. The probability that they contradict each other when asked to speak on a fact, is

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>EXERCISE 19.2>Q 18

If

P (B) = \frac{3}{4}, P (A \cap B \cap \bar{C}) = \frac{1}{3}

and

P (\bar{A} \cap B \cap \bar{C}) = \frac{1}{3}

. Find

P (B \cap C)

.

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>EXERCISE 19.2>Q 19

Five horses are in race. Mr.

A

selects two of the horses at random and bets on them. Find the probability that Mr.

A

selected the winning horse.

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>EXERCISE 14.2>Q 17

If

A

and

B

are two independent events such that

P (\bar{A} \cap B) = \frac{2}{15}

and

P (A \cap \bar{B}) = \frac{1}{6}

, then find

P (B)

.

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>EXERCISE 14.3>Q 20

The probability that a teacher will give an unannounced test during any class meeting is

\frac{1}{5}

. If a student is absent twice, then the probability that the student will miss at least one test, is

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Gamma Question Bank for Engineering Mathematics>Chapter 21 - Probability>EXERCISE 14.3>Q 21

Three letters are written to three different persons and addresses on the three envelopes are also written. Without looking at the addresses, the letters are kept in these envelopes. The probability that all the letters are not placed into their right envelopes is