Question

A die is thrown 400 times with the frequency for the outcomes one, two, three four five and six As given in the following table-
Outcomes-- 1,2,3,4,5,6
Frequency --72,65,70,71,63,59
Find tge probability of --
1.getting a number less than 3
2. Getting an outcome 6
3.getting a no. More than 4

Answer 1

Answer:

$p(a) = \frac{137}{400} \\ \\ p(b) = \frac{59}{400} \\ \\ p(c) = \frac{61}{200}$

Given:-

• A die is thrown 400 times with the frequency for the outcomes one, two, three four five and six As given in the following table-

$outcome \: \: \: \: \: \: frequency \\ 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 72 \\ 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 65 \\ 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 70 \\ 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 71 \\ 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 63 \\ 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 59$

To find:-

• Find the probability of --
• 1.getting a number less than 3
• 2. Getting an outcome 6
• 3.getting a no. More than 4

Solution:-

here,

total number of outcome =400

now ,

as per question

1.getting a number less than 3

so,

total number of out come less than 3 =72 + 65 = 137

$p(a) = \frac{number \: of \: outcome \: favourable \: }{total \: possible \: number \: of \: outcome} \\ \\ \: \: \: \: \: \: = \frac{137}{400}$

2) getting an out come 6

so total number kf out come 6 is = 59

$p(b) = \frac{number \: of \: outcome \: favourable \: }{total \: possible \: number \: of \: outcome} \\ \\ \: \: \: \: \: \: \: \: \: = \frac{59}{400}$

3)getting number more than 4

so total number od out come = 63+59 =122

$p(c) = \frac{number \: of \: outcome \: favourable \: }{total \: possible \: number \: of \: outcome} \\ \\ \: \: \: \: \: \: \: = \frac{122}{400} \: \: \: ......... (divide) \\ \\ \: \: \: \: = \frac{61}{200}$

Answer 2

p (Getting no. less than 3) =72+65/400=137/400

p(getting outcome 6) =59/400

p(getting no. more than 4) =63+59/400=122/400 or 61/200