1.

A two digit number is written atrandom (digit at 10s place is non-zero). The probability that thenumber will be even but smallerthan 40 is​

Answer»

\LARGE\underline\mathfrak{QueStion:}

ᴀ ᴛᴡᴏ ᴅɪɢɪᴛ ɴᴜᴍʙᴇʀ ɪs ᴡʀɪᴛᴛᴇɴ ᴀᴛ ʀᴀɴᴅᴏᴍ (ᴅɪɢɪᴛ ᴀᴛ 10s ᴘʟᴀᴄᴇ ɪs ɴᴏɴ ᴢᴇʀᴏ).ᴛʜᴇ ᴘʀᴏʙᴀʙɪʟɪᴛʏ ᴛʜᴀᴛ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴡɪʟʟ ʙᴇ ᴇᴠᴇɴ ʙɪᴛ sᴍᴀʟʟᴇʀ ᴛʜᴀɴ 40 ɪs?

\LARGE\underline\mathfrak{AnSwEr:}

ᴡᴇ ᴀʀᴇ ɢɪᴠᴇɴ ᴛʜᴀᴛ ᴛʜᴇʀᴇ ᴀʀᴇ ᴛᴏᴛᴀʟ 90 ɴʙʀs,

[ʜ :- 9 ssɪʙʟ ɪɢɪs ɪɴ sɴ sʟ × 10 ɪɢɪs ɪɴ sʟ = ʟ 90 ɴʙʀs]

ᴀɴᴅ ᴡᴇ ʜᴀᴠᴇ ᴛᴏ ғɪɴᴅ ᴛʜᴇ ᴘʀᴏʙᴀʙɪʟɪᴛʏ ᴏғ ɪɢɪ ɴʙʀ ʜ ɪs ʜsɴ ʀɴ

ʟs,

ʜ ʜ ɴs ʟ ɪɢɪ ғ ʜ ɴʙʀ ɪs ɴɴ ʀ[ ᴛᴇɴ's ᴘʟᴀᴄᴇ ᴅɪɢɪᴛ ≠ 0 ]

s ʟᴇᴛ's ʙɢɪɴ;

\LARGE\underline\mathfrak{Step \: by \: step \: explanation:}

ғʀʟ s;

{\boxed{\sf \orange{ P(E) \: = \: \frac{ No. \: of \: favourable \: outcomes}{No. \:  of \: total \:  outcomes} }}}

ɴ,ʟ ᴏᴜᴛᴄᴏᴍᴇs:-

ᴡᴇ ʜᴀᴠᴇ ᴛᴏ ғɪɴᴅ ᴘʀᴏʙᴀʙɪʟɪᴛʏ ғᴏʀ 90ᴏᴜᴛᴄᴏᴍᴇs ᴀs ɴᴜᴍʙᴇʀs,sᴏ ᴡᴇ ᴛᴀᴋᴇ

ɴᴏ. ᴏғ ᴛᴏᴛᴀʟ ᴏᴜᴛᴄᴏᴍᴇs = 90

ʟs,ᴘᴏssɪʙʟᴇ s :-

ᴛʜᴇ ᴘᴏɪɴᴛ ᴛʜᴀᴛ sʜᴏᴜʟᴅ ʙᴇ ɴᴏᴛɪᴄᴇᴅ ʜᴇʀᴇ ;

ᴡᴇ ʜᴀᴠᴇ ᴛᴏ ғɪɴᴅ ᴘʀᴏʙᴀʙɪʟɪᴛʏ ᴏғ ɴᴜᴍʙᴇʀ ʟᴇss ᴛʜᴀɴ 40,ᴀᴍᴏɴɢ 40 ɴᴜᴍʙᴇʀs ᴛʜᴇʀᴇ ᴀʀᴇ ᴏɴᴇ's ᴀs ᴡᴇʟʟ ᴀs ᴛᴇɴ's ᴘʟᴀᴄᴇ ᴅɪɢɪᴛs ɴᴜᴍʙᴇʀs

sᴏ,ᴡᴇ ᴛᴀᴋᴇ ᴅɪғғᴇʀᴇɴᴄᴇ ᴏғ ᴀʟʟ ᴛʜᴇsᴇ ᴀɴᴅ ᴡᴇ ɢᴇᴛ

\mapsto \normalsize\tt\ 40 \: - \: 9 \: - \: 1 \: = \: 30

ɴ s;

\mapsto \normalsize\tt\frac{30}{2} \: = \: 15

ɴ;

ɴᴜᴍʙᴇʀ ᴏғ ᴘᴏssɪʙʟᴇ ᴏᴜᴛᴄᴏᴍᴇs = 15

ʟs,

ʜᴇʀᴇ ᴡᴇ ᴛᴀᴋᴇ "ᴇ" ᴀs ᴇᴠᴇɴᴛ ᴀɴᴅ ᴛʜᴇ

ᴇᴠᴇɴᴛ = ᴄʜᴏᴏsɪɴɢ ᴏғ ᴀ ᴛᴡᴏ ᴅɪɢɪᴛ ᴀᴛ ʀᴀɴᴅᴏᴍ.

ʏʀ ᴀɴsᴡᴇʀ,ᴀᴄᴄᴏʀᴅɪɴɢ ɢɪᴠᴇɴ ;

\large\tt\ P(E) \: = \: \frac{15}{90} \: = \: \frac{1}{2}

{\boxed{\sf \blue{P(E) \: = \: \frac{1}{6} }}}



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