If you roll a dice once, what\'s the probability that it will show an even numbe

Question

If you roll a dice once, what's the probability that it will show an even number? An odd number? Assume that you flip a coin twice (assume independence) What's the probability that it will land heads once and tails once? What's the probability that it will land heads at least once? If you are told that one of the flips came up heads, what is the probability that both are heads? Determine which of the following statement is always true If A and B are independent, then they are also disjoint. P(A|B) + P(B|A) = 1 If P(A|B) = P(B|A), then A and B are independent If A and B are disjoint, then A and B cannot occur at the same time

Explanation / Answer

1) probabilty of showing even number =probability of odd number=3/6=1/2 as there are 3 even and 3 odd number

2)as there are 4 possibilty {head head; head tail ; tail head; tail tail}

a)probabilty of head and tail>

b)probability of head at least>

c)as one head comes in 3occasion, in which there are 2 heads in one ocassion ; hence probability =1/3

3)option D is correct as P(AnB)=0 is the required condition for disjoint

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