Question

Given that events "A" and "B" are independent, P(A)= 0.80 and P(A and B) = 0.24, what is P (B)?

Answer 1

Answer:  The correct options are

(1) (D) 0.30

(2) (A) 20%

(3) (C) 24.5%.

Step-by-step explanation:  We are given to answer all the following three questions.

(1) Given that A and B are independent events, where

$P(A)=0.80,~~P(A\cap B)=0.24,~~~P(B)=?$

We know that

if S and T are independent events, then

$P(S\cap T)=P(S)\times P(T).$

Therefore, we get

$P(A\cap B)=P(A)\cap P(B)\\\\\Rightarrow 0.24=0.80\times P(B)\\\\\Rightarrow P(B)=\dfrac{0.24}{0.80}\\\\\Rightarrow P(B)=0.30.$

Option (D) is CORRECT.

(2) Given that a weather forecaster predicts that their is 50% chance of rain on Saturday and a 40% chance of rain on Sunday.

We are to find the probability that it will rain both days.

Let X and Y represents the probabilities that it will rain on Saturday and Sunday respectively.

Then, we have

$P(X)=50\%=\dfrac{50}{100}=\dfrac{1}{2},\\\\\\P(Y)=40\%=\dfrac{40}{100}=\dfrac{2}{5}.$

Since X and Y are independent of each other, so the probability that it will rain both days is

$P(X\cap Y)=P(X)\times P(Y)=\dfrac{1}{2}\times\dfrac{2}{5}=\dfrac{1}{5}\times100\%=20\%.$

Option (A) is CORRECT.

(3) Given that a card is randomly drawn from a shuffled deck of cards and NOT REPLACED. A second card is drawn from the remaining shuffled cards.

We are to find the probability that both cards are RED.

Since there are 26 red cards in a pack of 52 cards, so the probability of drawing first red card is

$p_1=\dfrac{26}{52}=\dfrac{1}{2}.$

Without replacement, the probability of drawing second red card will be

$p_2=\dfrac{25}{51}.$

Therefore, the probability that both cards are red is

$p=p_1\times p_2=\dfrac{1}{2}\times\dfrac{25}{51}=\dfrac{25}{102}=0.245\times100\%=24.5\%.$

Option (C) is CORRECT.

Thus, (D), (A) and (C) are correct options.

Answer 2

Answer:

1. 0.30

2. 20%

3. is not 24.5%

Step-by-step explanation: