Question

6. The digits 1,2,3,4 and 5 are randomly arranged to form a three-digit number. If digits are not repeated, find the probability that the number is even and greater than 500? 7. A coin is tossed 10 times. Find the probability that at least one toss results in a tail. 8. A game is played using one die. If the die is rolled and shows 1,2 or 3, the player wins nothing. If the die shows 4 or 5, the player wins $3. If the die shows 6, the player wins $9. If there is a charge of $1 to play the game, what is the game's expected value? Describe what this means in practical terms?

Answer 1

Answer:

6)

Digits 1, 2, 3, 4, and 5 are randomly arranged to form a three-digit number Number of three digit numbers can be formed is 5 P3 ways
  

₅ P ₃ = 5! / ( 5 - 3 )!

= 5*4*3*2! / 2!

= 60

To get an even number and greater than 500 below conditions has to satisfy.

The number in the hundreds place should be 5 or above. So here five is the only option.

The number in units place should be even number Here even numbers are 2 and 4 So the number of possible chances is two.

You can select any number in tens place. Already we selected two numbers for hundreds place and units place so the number of chances are three (since three numbers remaining)

So total number of possible to select an even number and greater than 500 is l x 3 x 2

Probability that the number is even and greater than 500 is

= Favorable cases /  Total number of cases

= 1 * 3 *2 / 60

= 1 /10

= 0.1.

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