Question

Question 1

Answer 1

Answer with Step-by-step explanation:

1.We are given that  three events  A, B and C.

P(A)=0.26

P(B)=0.5

P(C)=0.45

P(A/B)=0.26

P(B/C)=0

P(C/A)=0.26

When two events A and B are independent then

$P(A\cap B)=P(A)\cdot P(B)$

If two events are mutually exclusive then

$P(A\cap B)=0$

We know that $P(A/B)=\frac{P(A\cap B)}{P(B)}$

$P(A\cap B)=P(A/B)\times P(B)$

$p(A\cap B)=0.26\times 0.5=0.13$

$P(A)\times P(B)=0.26\times 0.5=0.13$

Hence, $P(A\cap B)=P(A)\cdot P(B)$

Therefore, event A and B are independent.

$P(B\cap C)=0\times 0.45=0$

Therefore, events B and C are mutually exclusive.

$P(A\cap C)=0.26\times 0.26=0.0676$

$P(A)\times P(C)=0.26\times 0.45=0.117$

$P(A\cap C)\neq P(A)\cdot P(C)$

Hence, event A and C are neither independent nor mutually exclusive.

Answer: A and B are independent

B and C are mutually exclusive.

2.Let E be the event that  randomly chosen person exercises and D be the event that a randomly chosen person is on a diet.

According to question

We have to find P(D/E).

Answer : P(D/E)