In (a) and (b) below, say whether the statement is true, false, or meaningless,
ID: 3297115 • Letter: I
Question
In (a) and (b) below, say whether the statement is true, false, or meaningless, and explain briefly in each case. (a) If something has probability -1, it can't happen. (b) If something has probability 0.8, it can be expected to happen about four times as often as its opposite. (c) Two cards will be dealt off the top of a well-shuffled deck (without replacing the first card). You have a choice: (i) To win $1 if the first card is an ace. (ii) To win $1 if the first card is an ace, and the second card is an ace. Briefly explain which is better, intuitively and without calculating, and then work out both probabilities. (d) Two cards will be dealt off the top of a well-shuffled deck (without replacing the first card). You have a choice: (i) To win $1 if the first card is a club. (ii) To win $1 if the first card is a club, or the second card is a diamond.Explanation / Answer
a) Meaningless as probability cant be a negative number.
b) Yes, true
Opposite will have a P of 0.2, so, main case would happen 4 times as compared to the opposite.
c) (i) is better as it will have a greater probability or chance of happening.
P of first card ace = 4/52 = 1/13 = 0.077
P of first as well as second ace = 4/52 * 3/51 = 0.0045
d) (ii) will br good as 'or' means probabilities will be added.
P of first club = 13/52 = 0.25
P first club or second diamond = 0.5