Mary and Jane both secretly select one number from {1, 2, .. ., 10} and write it

Question

Mary and Jane both secretly select one number from {1, 2, .. ., 10} and write it down. (it's possible that they both select the same number). What is the probability that the number selected by Jane is strictly greater than the number selected by Mary? 3. Bob owns twenty different DVDs, among them three seasons of "Law and Order". If he randomly arranges all his DVDs on a shelf, what is the probability that the three "Law and Order" DVDs will all end up next to each other? 4. A Toyota dealership has recently received a shipment of ten 2017 Prius'. The cars are indistinguishable except for their color. Two of the cars are "blizzard pearl" (white) one car is "Sea glass pearl" (green), three cards are "silver metallic and the remaining cars are "magnetic grey". A dealership employee parks the ten cars in random order in a row. (a) What is the probability that the two white cars end up on the left and right ends of the row? (b) What is the probability that the cars of the same color will all stand next to each other? (c) Another employee backs up the company truck and damages two of the new cars. What is the probability that they were both magnetic grey?

Explanation / Answer

2)

There are total 10*10 = 100 combinations of numbers those can be selected by Mary and Jane.

possible combinations where Jane will have the number strictly greater than the number selected by Mary are 9+8+7+...+1 = 45

Hence the required probability = 45/100 = 0.45

3)

20 DVDs can be arranged in 20! ways.

Now, the condition is we need all the season of "Law and Order" together. Consider all 3 DVDs as one. Hence there are 18 number of DVDs to be arranged. This can be done in 18! ways. 3 DVDs can be arranged among themselves in 3! ways.

Hence total number of possible ways are 18! * 3!

Required probability = 18!*3! / 20! = (3*2*1)/(19*20) = 3/190

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