EXPERIMENTAL PROBABILITY PROBLEMS AND SOLUTIONS

Problem 1 :

Find the experimental probability of 

a) tossing a head with one toss of a coin if it falls 96 heads in 200 tosses.

b) Rolling a six with a die given when it was rolled 300 times, a six occurred 54 times.

Solution :

a) Let A be the event of getting head

Number of times getting head = 96

Total number of tosses = Relative frequency = 200

P(A) = 96/200

Doing the simplification, we get

P(A) = 12/25

b) Let A be the event of getting a six with a die

Number of times 6 occurred = 54

Number of tosses = 300

P(A) = 54 / 300

Problem 2 :

Find the experimental probability of rolling an odd number with a die if an odd number occurred 33 times when the die was rolled 60 times.

Solution :

Number of times die was rolled = 60

Number of times that the odd number occurred = 33

Required probability = 33/603

= 11/20

So, the required probability is 11/20.

Problem 3 :

Clem fired 200 arrows at a target and hit the target 168 times. Find the experimental probability of Clem hitting the target.

Solution :

Number of times hit the target = 200

Number of times it hits = 168

The required probability = 168/200

= 84/100

After the simplification, we get

= 21/25

Problem 4 :

Ivy has free range hens. Out of the first 123 eggs that they laid she found that 11 had double yolks. Calculate the experimental probability of getting a double yolk egg from her hens.

Solution :

Total number of eggs laid = 123

Number of eggs has double yolks = 11

The probability of getting number of eggs has double yolks

= 11/123

Problem 5 :

Jackson leaves for work at the same time each day. Over the period of 227 working days on his way to work he had to wait for the train at the railway crossing on 58 days. Calculate the experimental probability that Jackson has to wait for the train on his way to work.

Solution :

Total number of working days = 227

Number of days he had to wait = 58

The required experimental probability = 58 / 227

Problem 6 :

Ravi has a circular spinner marker P, Q and R on 3 equal sectors. Find the experimental probability of getting Q if the spinner was twirled 417 times and finished Q on 138 occasions.

Solution :

Number of times it was twirled = 417

Number of times finished Q = 138

The required probability = 138/417

Problem 7 :

Each time Claude shuffled a pack of cards before the game, he recorded the suit of the top card on the pack.

His result for 140 games were 34 hearts, 36 diamonds, 38 spade and 32 clubs 

Find the experimental probability that the top card of the shuffled pack is

a) heart    b)  club or diamond

Solution :

Total number of games = 140

a) Number of heart = 34

Probability of getting heart = 34/140

= 17/70

b) Number of club or diamond = 32 + 36

= 68

Probability of getting club or diamond = 68/140

= 17/35