Question

MC0102: A student has a nickel, dime, quarter, and half-dollar (yes - let's just pretend) in her pocket. If she pulls 3 coins out of her pocket without replacement, what is the sample space of simple events? Assume that the order that she pulls out the coins does not matter (so pulling N, D, Q is the same as pulling Q, D, N, etc.). N=Nickel, D=Dime, Q=Quarter, and H=Half-dollar.

	a.	12 outcomes {N, D, Q, H, N, D, Q, H, N, D, Q, H}
	b.	4 outcomes: {N, D, Q, H}
	c.	3 outcomes: {Coin1, Coin2, Coin3}
	d.	4 outcomes: {NDQ, NDH, NQH, DQH}
	e.	None of these MC0302: Which of the following are true about independent events A and B? I: Events A and B cannot both occur. II: Whether event A occurs has no impact on the probability of event B, and vice versa. III: P(A and B) = P(A) * P(B) a. I only b. II only c. III only d. I and II only e. I and III only f. II and III only g. I, II, and III h. None of these MC0402: Suppose there are two events, A and B. The probability of event A is P(A) = 0.3. The probability of event B is P(B) = 0.4. The probability of event A and B (both occurring) is P(A and B) = 0. Events A and B are: a. Complementary events b. The entire sample space c. Independent events d. Mutually exclusive events e. None of these

Answer 1

Hello

MC0102 OPTION D IS CORRECT -- 4 outcomes: {NDQ, NDH, NQH, DQH}

If she pulls out 3 coins from her pocket out of 4, lets' see it another way that she'll miss out only one coin in her pocket and she can do it in just 4 ways and can pull out NDQ,NDH,NQH,DQH.

MC0302 OPTION F IS CORRECT -- II and III only

Independent events are events whose occurance or non-occurance doesn't have any impact of occurance or non-occurance of the other. And P(A and B) = P(A)*P(B). But they both can occur together.

MC0402 OPTION D IS CORRECT -- Mutually Exclusive Events

P(A) = 0.3 , P(B)= 0.4

As, hence these can't be complementary events and these can't be entire sample space.

As, hence, these can't be independent events.

As , hence these are mutually exclusive envents, as mutually exclusive events are the events which can't occur together.

I hope this solves your doubt.

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