PROBLEMS ON EXPERIMENTAL PROBABILITY

The estimated experimental probability is the relative frequency of the outcome.

Example 1 :

Find the experimental probability of 

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

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

Solution :

(a)  Number of times it tosses  =  200

Number of times the coin shows head  =  96

P(getting a head)  =  96/200

(b)  Number of times the die was rolled  =  300

Number of times 6 appears  =  54

P(getting six)  =  54/300

Example 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 rolled  =  60

Number of times odd number occurred  =  33

P(getting odd number)  =  33/60

=  11/20

Example 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 arrows fired at a target  =  200

Number of arrows reached the target  =  168

P(hitting the target)  =  168/200

Example 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  =  123

Number of double yolk eggs  =  11

P(getting double yolk eggs)  =  11/123

Example 5 :

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

Solution :

Total number of working days  =  227

Number of days he wait for a train at the railway crossing  =  58

P(Jackson has to wait)  =  58/227

Example 6 :

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

Solution :

Total number of times the spinner was twirled  =  417

Number of times it is finished with Q  =  138

P(getting Q)  =  138/417

Example 7 :

Each time Claude shuffled a pack of cards before a game, he recorded the suit of the top card of the pack His results for 140 games were 34 Hearts, 36 Diamonds, 38 Spades and 32 Clubs.

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

(a) a Heart  (b) a Club or Diamond

Solution :

Total number of games played  =  140

In which, number of times it shows the top card as 

heart  =  34

diamond  =  36

spades  =  38

clubs  =  32

(i)  P(getting heart at top)  =  34/140

(ii)  P(club or diamond)  =  (32+36)/140

=  68/140

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