Question

1. Consider drawing a single card from a well shuffled 52-card deck. Let E1 be an event of getting a heart card and E2 be an event of getting a face card. Find P(E1UE2). 2. Two balls are drawn in succession, without replacement, from a box containing 4 blue and 6 white balls of the same sizes. What is the probability of drawing a blue ball on the first draw and a white ball on the second drawn?

Answer 1

1) Find P(E1UE2)
E1 probability= 1/2
There are 26 red cards in a 52 card deck, so the probability of choosing a red card is = 26/52 = 1/2
E2 probability= 12/ 52 or 3/13
The face cards are: Jacks, Queens, and Kings. There are four suits, so in each suit there are one jack, one queen and one king. The probability is 3 x 4= 12 divided by the total number of cards.

2)the probability of drawing a blue ball on the first draw: 4 /10
the probability of drawing a white ball on the second drawn: 6/9 (because there is less one ball from the previous draw).
the probability of the cases together is 4/15 ( 4 /10 x 6/9) since they are independent cases.