Question

Open in App

Verified by Toppr

$S=HHHH,HHHT,HHTH,HTHH,THHH,HHTT,HTTH,TTHH,HTHT,THTH,THHT,HTTT,THTT,TTHT,TTTH,TTTT$

$∴n(S)=16$

Since, the coin is tossed four times there can be a maximum of $4$ heads .

When $4$ heads turns up, $Re1+Re1+Re1+Re1=Rs4$ is the gain.

When $3$ heads and $1$ tail turn up, $Re1+Re1+Re1−Rs1.50=Rs3−Rs1.50=Rs1.50$ is the gain.

When $2$ heads and $2$ tails turns up, $Re1+Re1−Rs1.50−Rs1.50=−Re1$, i.e., Re $1$ is the loss.

When $1$ head and $3$ tails turn up,$Re1−Rs1.50−Rs1.50−Rs.1.50=−Rs3.50$, i.e., Rs $3.50$ is the loss.

When $4$ tails turn up, $−Rs1.50−Rs1.50−Rs1.50−Rs1.50=−Rs6.00$ i.e., Rs $6.00$ is the loss.

The person wins Rs $4.00$ when $4$ heads turn up i.e., when the event ${HHHH}$ occurs.

$∴$Probability (of winning Rs $4.00$)= $161 $

When $4$ heads turns up, $Re1+Re1+Re1+Re1=Rs4$ is the gain.

When $3$ heads and $1$ tail turn up, $Re1+Re1+Re1−Rs1.50=Rs3−Rs1.50=Rs1.50$ is the gain.

When $2$ heads and $2$ tails turns up, $Re1+Re1−Rs1.50−Rs1.50=−Re1$, i.e., Re $1$ is the loss.

When $1$ head and $3$ tails turn up,$Re1−Rs1.50−Rs1.50−Rs.1.50=−Rs3.50$, i.e., Rs $3.50$ is the loss.

When $4$ tails turn up, $−Rs1.50−Rs1.50−Rs1.50−Rs1.50=−Rs6.00$ i.e., Rs $6.00$ is the loss.

The person wins Rs $4.00$ when $4$ heads turn up i.e., when the event ${HHHH}$ occurs.

$∴$Probability (of winning Rs $4.00$)= $161 $

The person wins Rs $1.50$ when $3$ heads and one tail turn up i.e., when the event ${HHHT,HHTH,HTHH,THHH}$ occurs

$∴$Probability (of winning Rs $1.50$) = $164 =41 $

The person loses Re $1.00$ when $2$ heads and $2$ tails turn up i.e., when the event ${HHTT,HTTH,TTHH,HTHT,THTH,THHT}$ occurs

$∴$ Probability (of losing Re 1.00) = $166 =83 $

The person loses Rs $3.50$ when $1$ head and $3$ tails turn up i.e., when the event ${HTTT,THTT,TTHT,TTTH}$ occurs

Probability (of losing Rs $3.50$) = $164 =41 $

The person loses Rs $6.00$ when $4$ tails turn up i.e., when the event ${TTTT}$ occurs

Probability (of losing Rs $6.00$) = $161 $

Solve any question of Probability with:-

0

0