Question

Please provide the solution to the below problems:


In a certain state lottery, a player selects four different numbers from 1 through 30. Find the probability that a single choice of four numbers wins the lottery, assuming the order of the numbers is not important.

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A club consisting of 20 members wishes to form a four-member committee. In how many ways can this be done?


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A jar contains 4 red balls and 6 green balls. A second jar contains 5 red balls and 8 black balls. If we select one ball from each jar, what is the probability of obtaining 1 red ball and 1 black ball?


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What is the probability of flipping a coin five times and obtaining exactly three heads?

Answer 1

You are choosing 4 from 30 numbers
= C(30,4) = 30!/(4!26!) = 27405
one of those will be correct
prob(correct #) = 1/27405

2. C(20,4) = ...

3. You don't say which jar we choose from first
but the first jar does not contain a black ball, so the order must be jar1, then jar 2
prob(red,black) = (4/10)(8/13) = 16/65

4. Prob(3 heads out of 5)
= C(5,3) (1/2)^3 (1/2)^2
= 10(1/32) = 5/16