Question

Two groups performed an experiment separately by tossing a coin in the air. Group P performed 50 trials and group Q performed 100 trials. Each group recorded the results in the table below:

Group Heads Tails
P 35 15
Q 53 47
What conclusion can be drawn about the number of trials and the probability of the coin landing on heads or tails?
The experimental probability and the theoretical probability for group P is the same.

The experimental probability and the theoretical probability for group Q is the same.

The experimental probability is closer to the theoretical probability for group Q than group P.

The experimental probability is closer to the theoretical probability for group P than group Q.

Answer 1

Theoretical probability;

Head = 1/2 or 50%

Tail = 1/2 or 50%

Group Heads Tails Total

A 35 15 50

B 53 47 100

Experimental probability:

Group P:

Heads : 35/50 = 70%

Tails: 15/50 = 30%

Group Q:

Head: 53/100 = 53%

Tails: 47/100 = 47%

The experimental probability and the theoretical probability for group Q is the same

Answer 2

The conclusion that can be drawn about the number of trials and probability of the coin landing on heads or tails is:

• The experimental probability is closer to the theoretical probability for group Q than group P.

Explanation:

We know that the theoretical probability for choosing a coin on heads or tails is:

1/2=50%

( Since, there are only two possibilities on tossing a coin either head or tail comes up)

Now, for group P the experimental frequency is:

Group Heads Tail

P 35 15

Hence, Probability(getting head)=35/50=0.7

in percent it is: 70%

and the Probability(getting tail)=15/50=0.3

in percent it is: 30%

Similarly,

Group Heads Tail

Q 53 47

Hence, Probability(getting head)=53/100=0.53

in percent it is: 53%

and the Probability(getting tail)=47/100=0.47

in percent it is: 47%

• The experimental probability is closer to the theoretical probability for group Q than group P.