You visited us 1 times! Enjoying our articles? Unlock Full Access!

Bayes' Theorem

Four fair dic...

Question

Four fair dice $D_{1}, D_{2}, D_{3}$ and $D_{4}$ , each having six faces numbered $1, 2, 3, 4, 5$ and $6$ , are rolled simultaneously. The probability that $D 4$ shows a number appearing on one of $D_{1}, D_{2}$ and $D_{3}$ is

\frac{127}{216}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{91}{216}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{108}{216}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{125}{216}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{91}{216}$
Required probability
= Getting equal number on two dice + equal number on three dice + equal number on four dice

$= \frac{^{6} C_{1} \times 3 \times 5 \times 5}{6^{4}} + \frac{^{6} C_{1} \times 3 \times 5}{6^{4}} + \frac{^{6} C_{1}}{6^{4}} = \frac{91}{216}$

Suggest Corrections

Similar questions

Q. Four fair dice

D_{1}, D_{2}, D_{3}

and

D_{4}

, each having six faces numbered

1, 2, 3, 4, 5

and

6,

are rolled simultaneously. The probability that

D_{4}

shows a number appearing on one of

D_{1}, D_{2}

and

D_{3}

Four fair dice $D_{1}, D_{2}, D_{3} a n d D_{4}$ each having six faces numbered 1, 2, 3, 4, 5 and 6 are rolled simultaneously. The probability that $D_{4}$ shows a number appearing on one of $D_{1}, D_{2} a n d D_{3}$ , is ?

Q. Four fair dice

D_{1}, D_{2}, D_{3}

and

D_{4}

each having six faces numberd

1, 2, 3, 4, 5

and

6,

are rolled simultaneously. The probability that

D_{4}

shows a number appearing on one of

D_{1}, D_{2}

and

D_{3}

Q. If

1, d_{1}, d_{2}, d_{3}, d_{4}

are roots of

x^{5} = 1

then the value of expression :

E = \frac{ω - d_{1}}{ω^{2} - d_{1}} \cdot \frac{ω - d_{2}}{ω^{2} - d_{2}} \cdot \frac{ω - d_{3}}{ω^{2} - d_{3}} \cdot \frac{ω - d_{4}}{ω^{2} - d_{4}}

is
[Here

ω

is the cube root of unity]

D1, D2, D3 and D4 are rectangles with areas $8 m^{2}, 6 m^{2}, 9 m^{2} a n d 4 m^{2}$ respectively. Which is the 'biggest' rectangle?

Join BYJU'S Learning Program

Four fair dice D1,D2,D3 and D4, each having six faces numbered 1,2,3,4,5 and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D1,D2 and D3 is

The correct option is B 91216 Required probability = Getting equal number on two dice + equal number on three dice + equal number on four dice =6C1×3×5×564+6C1×3×564+6C164=91216

Four fair dice $D_{1}, D_{2}, D_{3}$ and $D_{4}$ , each having six faces numbered $1, 2, 3, 4, 5$ and $6$ , are rolled simultaneously. The probability that $D 4$ shows a number appearing on one of $D_{1}, D_{2}$ and $D_{3}$ is

The correct option is B $\frac{91}{216}$
Required probability
= Getting equal number on two dice + equal number on three dice + equal number on four dice

$= \frac{^{6} C_{1} \times 3 \times 5 \times 5}{6^{4}} + \frac{^{6} C_{1} \times 3 \times 5}{6^{4}} + \frac{^{6} C_{1}}{6^{4}} = \frac{91}{216}$