Question

A weather forecaster predicts that their is 50% chance of rain on Saturday and a 40% chance of rain on Sunday. If these probabilities are correct, what is the probability that it will rain both days?

Group of answer choices:

20%

45%

10%

90%



A card is randomly drawn from a shuffled deck of cards and NOT REPLACED. A second card is drawn from the remaining shuffled cards. What is the approximate probability that both cards are RED?

Group of answer choices:

49%

50%

24.5%

25%

Answer 1

20%.

24.5 %.

Explanation:

As the 2 events are independent we multiply the individual probabilities:

Answer is 0.50 * 0.40 = 0.20.

Prob First card is red = 26/52 = 1/2.

Prob(second card is red) = 25/51

The required probability = 1/2 * 25/51

= 25/102.

= 24.5 %.

Answer 2

Answer with explanation:

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

i.e. P(Saturday)= 0.50 and P(Sunday)= 0.40

Since rain happen on each day is independent of previous days.

Then, the probability that it will rain both days will be :-

P(Saturday and Sunday) = P(Saturday)×P(Sunday)

`=50*0.40=0.20`

Hence, the probability that it will rain both day= 20%

ii) Total number of cards in deck = 52

Number of red cards = 26

Let A be the event of drawing first red card and B be the event of drawing second red card.

Since , probability for any event =
`\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}`

Then ,
`P(A)=(26)/(52)=(1)/(2)`

After getting first card , total cards left = 51

Total red cards left = 25

Then, Probability of getting second red card
`P(B|A)=(25)/(51)`

Using conditional probability formula
`P(B|A)=(P(A\cap B))/(P(A))`, we have

`P(A\cap B)=P(B|A)* P(A)\\\\=(25)/(51)*(1)/(2)\\\\=0.245098039216\approx0.245=24.5\%`

Hence, the approximate probability that both cards are RED= 24.5%