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
We know that
if S and T are independent events, then
Therefore, we get
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
Since X and Y are independent of each other, so the probability that it will rain both days is
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
Without replacement, the probability of drawing second red card will be
Therefore, the probability that both cards are red is
Option (C) is CORRECT.
Thus, (D), (A) and (C) are correct options.